A lecture organized in cooperation with the Mathematical Institute of the Czech Academy of Sciences.

]]>Application to GSSI post doctoral research grantshttp://more.karlin.mff.cuni.cz/application-to-gssi-post-doctoral-research-grants/
Mon, 24 Apr 2017 06:14:46 +0000http://more.karlin.mff.cuni.cz/?p=1744read more]]>GSSI offers 5 positions for research activity in the fields of interest of
the Institute There is no age limit for applicants; however eligible
candidates in Mathematics must have earned their PhD not earlier than
January 1, 2012.

Candidates who are preparing their doctoral thesis are eligible to apply;
however, they must have obtained their Ph.D degree before taking up their
appointment with GSSI.

]]>MORE: talk by Miroslav Rozložníkhttp://more.karlin.mff.cuni.cz/more-talk-by-miroslav-rozloznik/
Fri, 21 Apr 2017 08:37:15 +0000http://more.karlin.mff.cuni.cz/?p=1741read more]]>The talk On GMRES for singular systems, by Miroslav Rozložník will be held on Monday April 24, 2017 at 9:00 in room K4.

Abstract:

In this talk we study the numerical behavior of the generalized minimal residual (GMRES) method for solving singular linear systems. GMRES determines a solution without breakdown in theory in the two cases: the coefficient matrix is symmetric in its range space (EP); its range space and null spaces are disjoint (GP). We show how the inconsistency of a linear system and the principal angles between the range o A and the range o A^T affect the conditioning of the extended Hessenberg matrix in the Arnoldi decomposition and the accuracy of computed iterates. We compare GMRES with the range restricted GMRES (RR-GMRES) method and the simpler GMRES method. Numerical experiments show typical behavior of GMRES in the EP and GP cases.

]]>Workshop on A posteriori error analysis, adaptivity and advanced applicationshttp://more.karlin.mff.cuni.cz/workshop-on-a-posteriori-error-analysis-adaptivity-and-advanced-applications/
Wed, 12 Apr 2017 14:04:47 +0000http://more.karlin.mff.cuni.cz/?p=1738read more]]>We wish to bring your attention to the workshop on A posteriori error analysis, adaptivity and advanced applications, to be held on Thursday 4th May and Friday 5th May 2017, at the Inria Paris research centre in Paris.

The core topics include a posteriori error estimation and adaptive methods for nonlinear partial differential equations and evolutionary problems, for a broad range of numerical methods including high-order methods.

Registration is free but compulsory, and it gives access to the talks and coffee breaks. You may register directly by emailing your name and institution to the organisers at organisers_aposterioriworkshop2017@inria.fr

The efficient solution of large linear least squares problems in which the system matrix A contains rows with very different densities is challenging. There have been many classical contributions to solving this problem that focus on direct methods; they can be found in the monograph by Ake Bjorck. Such solvers typically perform a splitting of the rows of A into two row blocks, As and Ad. The block As is such that the sparse factorization of the normal matrix A^T_s As is feasible, while the rows in the block Ad have a relatively large number of nonzero entries. These dense rows are initially ignored, a factorization of the sparse part is computed using a sparse direct solver and then the solution updated to take account of the omitted dense rows.

There are two potential weaknesses of this approach. First, in practical applications the number of rows that contain a significant number of entries may not be small. Processing some of the denser rows separately may improve performance. Furthermore, large-scale problems require the use of preconditioned iterative solvers. A straightforward proposal to precondition the iterative solver using only an incomplete factorization of the sparse block while discarding the dense block may not lead to any success. In this presentation, we propose processing As separately within a conjugate gradient method using an incomplete factorization preconditioner combined with the factorization of a dense matrix of size equal to the number of rows in Ad. Problems arising from practical applications are used to demonstrate the potential of the new approach.

We consider a convection-diffusion boundary value problem (1D, convection dominated) with Dirichlet boundary conditions. Because of the occurrence of boundary layers in the solution, such problems are difficult to solve numerically. Standard discretization techniques typically cannot resolve the layers and have to be stabilized in order to yield an acceptable numerical solution. Here we consider discretizations using a Shishkin mesh, which clusters mesh points in the layer instead of putting them equidistantly over the whole region, leading to linear algebraic systems with highly nonnormal matrices. In this talk we are interested in solving such systems using the GMRES method and the multiplicative Schwarz method.

Multilevel adaptive methods represent a very large class of approaches towards solving large scale problems.
They can be used either as stand-alone solvers, or as preconditioning in combination, e.g., with Krylov subspace methods.
In this working seminar we aim at discussing an associate abstract setting in the frame of operator preconditioning.